On the first 4 exams of her physics class, Nadia got an average score of 80. What does she need on the next exam to have an overall average of 82?
Answer: Let her score on the next exam be $x$ The sum of all of her scores is then $4 \cdot 80 + x$ The same sum must also be equal to $5 \cdot 82$ Solve: $x = 5 \cdot 82 - 4 \cdot 80 = 90$.